基于牛顿迭代法的S形加减速时间算法研究

中国机械工程 ›› 2015, Vol. 26 ›› Issue (7): 912-916,942.

基于牛顿迭代法的S形加减速时间算法研究

杨亮亮1,2;许守金1,2;史伟民1,2;葛宏伟1,2

1.浙江省现代纺织装备技术重点实验室,杭州,310018
2.浙江理工大学,杭州,310018

出版日期:2015-04-10 发布日期:2015-04-24
基金资助:
国家自然科学基金资助项目（51305404）；国家科技支撑计划资助项目(2013BAF05B01)

Research on Algorithm of S_shape Acceleration and Deceleration Time Based on Newton Iterative Method

Yang Liangliang1,2;Xu Shoujin1,2;Shi Weimin1,2;Ge Hongwei1,2

1.Zhejiang Provincial Key Lab of Modern Textile Machinery & Technology,Hangzhou,310018
2.Zhejiang Sci-Tech University,Hangzhou,310018

Online:2015-04-10 Published:2015-04-24
Supported by:
National Natural Science Foundation of China（No. 51305404）;The National Key Technology R&D Program（No. 2013BAF05B01）

摘要/Abstract

摘要：

S形加减速控制涉及求解多元高次方程或者不等式，且要求求解出来的最终解是非负数，为此根据时间最优原则和速度、加速度的限制条件，把S形加减速控制中所涉及的五元非线性方程组分解为2个二元非线性方程组和1个一元线性方程。采用牛顿迭代法和迭代修正的方式逐步求解出符合要求的加减速时间，进而求出速度曲线，进行插补运算。仿真与实验结果证明,该算法简明高效、运行稳定，能够满足高速高精数控要求。

关键词: S形加减速控制, 五元非线性方程, 牛顿迭代法, 时间最优原则

Abstract:

Due to S_shape acceleration and deceleration control involved solving multiple high-order equation or inequality, and the final solution was non negative, so that it was difficult to calculate.Therefore nonlinear equations of five independent variables of S_shape acceleration and deceleration control were decomposed into two nonlinear equations of two independent variables and a linear equation according to time optimal principle and the constraints of speed, acceleration. The final solutions were obtained by Newton iterative method and the iterative correction method then the velocity curve and interpolation algorithm were found. The simulation and experiments were presented to prove that the algorithm is simplicity, stable operation and the ability to meet the requirements of high speed and high precision of computer numerical control.

Key words: S_shape acceleration and deceleration control;nonlinear equations of , five , independent variables;Newton iterative method;time optimal , principle

中图分类号:

TP391

杨亮亮, 许守金, 史伟民, 葛宏伟, . 基于牛顿迭代法的S形加减速时间算法研究[J]. 中国机械工程, 2015, 26(7): 912-916,942.

Yang Liangliang, Xu Shoujin, Shi Weimin, Ge Hongwei, . Research on Algorithm of S_shape Acceleration and Deceleration Time Based on Newton Iterative Method[J]. China Mechanical Engineering, 2015, 26(7): 912-916,942.

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